If this calculator from the american wood council is to be believed and if my assumptions about your materials and load are correct the max span is about 10ft for a pine 2x6.
Maximum span 2x6 roof rafter.
Douglas fir maximum horizontal roof rafter span for lumber grade selected structural and no.
An syp 2 6 rafter at 24 o c.
40 psf allowable spans for df 1 floor girders df larch 2x8 2x10 2x12 2x6 4 12 7 3 oct 28 2014 what is the maximum span for a beam made of 2 2x8 1 2 inch plywood sandwiched and 2 2x4 flat top and bottom to be used similar to top plates to support only a metal roof and.
Span calculator for wood joists and rafters also available for the android os.
These numbers are for roofs supporting light loads of 20 pounds for square foot.
Another option are 2 x 8 rafters spaced 24 inches o c.
Maximum rafter spans for a patio roof in areas with mild climates patio roofs are generally designed for loads of 30 psf pounds per square foot.
This table agrees that 10 12ft is the max span for typical grade lumber at typical spacings for a 5psf dead load.
Looking through the center of the table we can find a couple of options.
Dead load weight of structure and fixed loads 15 lbs ft 2.
1 ft 0 3048 m.
1 psf lb f ft 2 47 88 n m 2.
8 2 rafter slope 2x6 2x8 2x10 dead load up to 10 psf live load.
Live load is weight of furniture wind snow and more.
The table states that 2 x 6 rafters spaced 16 inches on center o c can span a maximum distance of 13 feet 5 inches.
Also available for the android os.
That means it can span a total length of over 26 for a gable roof.
For heavy roofs or in areas with substantial snowfall or winds call your local building department for code requirements.
For example in the rafter span table below the highlighted cell in the 40 live load table indicates that 2 x 8 southern yellow pine joists that have a grade of 2 that are spaced 24 apart can have a maximum span of 10 feet 3 inches 10 3 if designing for a live load of 40 lbs ft 2.
2 are indicated below.
An spf roof at the same spacing and lumber size will span 11.